{"title":"超椭圆分量的长度谱","authors":"Corentin Boissy, Erwan Lanneau","doi":"10.4171/jems/1150","DOIUrl":null,"url":null,"abstract":"We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmüller geodesic flow restricted to the hyperelliptic connected components of the strata of Abelian differentials, settling a question of [Far06]; This is the first description of the systole in any component of any stratum outside of genus two and three. We stress that all proofs and computations can be performed without the help of a computer. As a byproduct, our methods give a way to describe the bottom of the lengths spectrum of the hyperelliptic components and we provide a picture of that for small genera.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"83 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lengths spectrum of hyperelliptic components\",\"authors\":\"Corentin Boissy, Erwan Lanneau\",\"doi\":\"10.4171/jems/1150\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmüller geodesic flow restricted to the hyperelliptic connected components of the strata of Abelian differentials, settling a question of [Far06]; This is the first description of the systole in any component of any stratum outside of genus two and three. We stress that all proofs and computations can be performed without the help of a computer. As a byproduct, our methods give a way to describe the bottom of the lengths spectrum of the hyperelliptic components and we provide a picture of that for small genera.\",\"PeriodicalId\":50003,\"journal\":{\"name\":\"Journal of the European Mathematical Society\",\"volume\":\"83 1\",\"pages\":\"\"},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the European Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/jems/1150\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the European Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1150","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We propose a general framework for studying pseudo-Anosov homeomorphisms on translation surfaces. This new approach, among other consequences, allows us to compute the systole of the Teichmüller geodesic flow restricted to the hyperelliptic connected components of the strata of Abelian differentials, settling a question of [Far06]; This is the first description of the systole in any component of any stratum outside of genus two and three. We stress that all proofs and computations can be performed without the help of a computer. As a byproduct, our methods give a way to describe the bottom of the lengths spectrum of the hyperelliptic components and we provide a picture of that for small genera.
期刊介绍:
The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS.
The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards.
Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004.
The Journal of the European Mathematical Society is covered in:
Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.